# The Fundamental Difference in Interpretations of Quantum Mechanics - Comments

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#### Fra

I think this discussion has many components, not sure which post rubis post related to.

For the record My core issue is not the principle of information update as such, i agree is the most natural component. My issues are different and more subtle.

My previous point of emergence did not refer to the collapse, it rather referred to to the rule of evolution in between updates.
The real quation about quantum theory is: Why does it make sense to have non-commuting observables in the first place?
The way i see it (inference interpretation), is because it allows the the observer to maximise its predictive power, when computing the expectation from the state of information. And this stabilises the observer from the destabilising environment.

It can be understood as datacompression of the abduced rules of expectation.

I think this can be described mathematically as well. But it requires a different foundation and framework pf physics, which is not yet in place. But developing that goes hand in hand with understanding and vague insight.

/Fredrik

#### stevendaryl

Staff Emeritus
What we directly observe in a measurement device are only macroscopic (what I called ''classical'') observables, namely the expectation values of certain field operators. These form a vast minority of all conceivalbe observables in the conventional QM sense. For example, hydromechanics is derived in this way from quantum field theory. Everyone knows that hydromechanics is highly chaotic in spite of the underlying linearity of the Schroedinger equation defining (nonrelativistic) quantum field theory from which hydromechanics is derived. Thus linearity in a very vast Hilbert space is not incompatible with chaos in a much smaller accessible manifold of measurable observables.
I think that's a very interesting subject--the reconciliation of the linearity of Schrodinger's equation with the chaotic nonlinearity of macroscopic phenomena. But I really don't think that chaos in the macroscopic world can explain the indeterminism of QM. In Bell's impossibility proof, he didn't make any assumptions about the complexity of the hidden variable $\lambda$, or the difficulty of computing measurement outcomes from $\lambda$, or the sensitivity of the outcomes to $\lambda$.

#### A. Neumaier

I really don't think that chaos in the macroscopic world can explain the indeterminism of QM. In Bell's impossibility proof, he didn't make any assumptions about the complexity of the hidden variable $\lambda$, or the difficulty of computing measurement outcomes from $\lambda$, or the sensitivity of the outcomes to $\lambda$.
Bell doesn't take into account that a macroscopic measurement is actually done by recording field expectation values. Instead he argues with the traditional simplified quantum mechanical idealization of the measurement process. The latter is known to be only an approximation to the quantum field theory situations needed to be able to treat the detector in a classical way. Getting a contradiction from reasoning with approximations only shows that at some point the approximations break down.

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#### vanhees71

Gold Member
His philosophy (what you called ''wild speculations'') lead him in 1925 to the discovery of the canonical commutation relations.
This was Born, and it was not philosophy but good knowledge of the math behind Heisenberg's ingenious idea. Not everything what Heisenberg did was philosophical gibberish but he also did some physics for which he rightfully got the Nobel prize in the early 1930ies.

#### A. Neumaier

This was Born, and it was not philosophy but good knowledge of the math behind Heisenberg's ingenious idea.
It was Born and Jordan. But Heisenberg had the ingenious idea - a philosophical feat!
Born and Jordan said:
Die mathematische Grundlage der H e i s e n b e r g s c h e n Betrachtung ist das M u l t l p l i k a t i o n s g e s e t z der quantentheoretisehen Größen, das er dutch eine geistreiche Korrespondenzbetrachtung erschlossen hat.
Werner Heisenberg said:
Bei dieser Sachlage scheint es geratener, jene Hoffnung auf eine Beobachtung der bisher unbeobachtbaren Größen (wie Lage, Umlaufszeit des Elektrons) ganz aufzugeben, gleichzeitig also einzuräumen, daß die teilweise Übereinstimmung der genannten Quantenregeln mit der Erfahrung mehr oder weniger zufälllig sei, und zu versuchen, eine der klassischen Mechanik analoge quantentheoretische Mechanik auszubilden, in welcher nur Beziehungen zwischen beobachtbaren Größen vorkommen.
This is pure philosophy - the attempt to reframe concepts to make sense of formerly apparently meaningless (or contradictory) concepts.

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#### vanhees71

Gold Member
Well, this "Korrespondenzbetrachtung" I'd still call physical rather than philosophical heuristics (as Einstein's "heuristic aspect" of the photoelectric-effect paper was physical rather than philocophical), but that's a bit semantics. Thanks anyway for pointing to the paper. It's interesting that this was written without Heisenberg. There's also the "Dreimännerarbeit", which is the 2nd part written with Heisenberg:

#### Stephen Tashi

When you have a distribution $\rho(x)$ at time $t$, then if you have gotten to know that $x\in A$, you multiply $\rho(x)$ by the characteristic function $\chi_A(x)$.
What that mathematical procedure represents is a matter of interpretation. It looks like we are computing an un-normalized version of a probability density representing "the probability that $X =x$ given $X \in A$". and interpreting "$X \in A$" to mean "the event $X \in A$ actually happened".

My point is that the interpretation of a conditional probability in terms of some event actually happening is not formalized in the mathematical theory of probability. The same comment applies to when we apply probability theory to compute "The probability a fair die lands a 6 given the event that the die showed an even number". The measure theoretic approach to probability theory does not formally define what it means for an event to "actually happen" or "be observed" etc. What the measure theoretic approach gives us is a definition of conditional probabilities in terms of a procedure for computing them from other probabilities.

Whether we are talking about the fancy mathematics of stochastic processes or the mathematics of a coin toss, there is the common theme of a "collapse" of a probability distribution - to a single outcome or to a conditional probability distribution when we interpret the mathematics. So one question is: Why is such a collapse of a probability distribution in a "classical" setting any more of a conceptual problem than the collapse of a wave function in QM?

I'm not asking that as a rhetorical question. I'd really like to hear about other problematic aspects of wave function collapse - if there are any.

----

As to how the interpretation of collapse meets relativity, I don't see that special relativity adds any new conceptual problems. General relativity adds the conceptual problem that collapse must be defined without some reference to absolute time. One article that deals with this is Collapse of Probability Distributions in Relativistic Spacetime by Hans Ohanian https://arxiv.org/pdf/1703.00309.pdf. It's notable that the solution given for where probability distributions collapse is the same for wave function collapse. So I don't see that wave function collapse added any conceptual problems that weren't already present in probability distribution collapse - at least from the viewpoint of that paper.

#### A. Neumaier

Thanks anyway for pointing to the paper. It's interesting that this was written without Heisenberg.
I added to the previous post a link to Heisenberg's first paper that started it all,and a quote from it that shows the philosophy that went into Heisenberg's ingenious idea.

#### vanhees71

Gold Member
Well, sure. So if you call this philosophy rather than physics then there's indeed some valuable physics originating from philosophy ;-)). Amazing!

#### lightarrow

The real quation about quantum theory is: Why does it make sense to have non-commuting observables in the first place?
Can something like "because a measurement, in general, changes the quantum sistem's state, so if we measure the observable A and then the observable B, the final state will be different than when we measure B first and then A" be an answer, given that there is "some relation" from a measurement of the observables A or B on a state |psi> and computing A|psi> and B|psi>?

--
lightarrow

#### junjunjun233

Bell doesn't take into account that a macroscopic measurement is actually done by recording field expectation values. Instead he argues with the traditional simplified quantum mechanical idealization of the measurement process. .
Will there be any implication of the observed value? Especially the dynamics on Quantum state. Like some limitations on visual aspect.

Like for instance. Quantum clock in a superposition of energy eigenstates, the mass–energy equivalence leads to a trade-off between the possibilities for an observer to define time intervals at the location of the clock and in its vicinity. In the sense that it does not depend on the particular constitution of the clock, and is a necessary consequence of the superposition principle and the mass–energy equivalence. In SR, some aspect of observations changes visually under extreme gravitational field or travelling at certain speed.

Are their any particular visual phenomenon in QM when observing quantum level?

https://phys.org/news/2017-03-blurred-quantum-world.html#jCp

..aslav Brukner from the University of Vienna and the Institute of Quantum Optics and Quantum Information demonstrated a new effect at the interplay of the two fundamental theories. According to quantum mechanics, if we have a very precise clock its energy uncertainty is very large. Due to general relativity, the larger its energy uncertainty the larger the uncertainty in the flow of time in the clock's neighbourhood. Putting the pieces together, the researchers showed that clocks placed next to one another necessarily disturb each other, resulting eventually in a "blurred" flow of time. This limitation in our ability to measure time is universal, in the sense that it is independent of the underlying mechanism of the clocks or the material from which they are made. "Our findings suggest that we need to re-examine our ideas about the nature of time when both quantum mechanics and general relativity are taken into account", says Esteban Castro, the lead author of the publication.

#### meopemuk

There is nothing contradictory about having two types of time evolution (unitary evolution, collapse).
I totally agree. There is no deep difference between quantum collapse and classical "collapse" of probability distributions. The only difference is that in classical physics the probabilities are results of our ignorance or laziness (the underlying dynamics is supposed to be predictable), but in quantum physics there is an additional fundamental and irreducible component of randomness/probabilities in the underlying dynamics (God plays dice).

The real quation about quantum theory is: Why does it make sense to have non-commuting observables in the first place?
I am very happy with the explanation provided by "quantum logic". I think this is a very beautiful piece of theory, which answers all questions about quantum foundations in the most satisfying way.

The original paper:
G. Birkhoff and J. von Neumann, "The logic of quantum mechanics", Ann. Math. 37 (1936), 823

A recent review:
L. Curcuraci, "Why do we need Hilbert spaces?", arXiv:quant-ph/1708.08326

Eugene.

#### bhobba

Mentor
but in quantum physics there is an additional fundamental and irreducible component of randomness/probabilities in the underlying dynamics (God plays dice).
This is exactly why people should study a few interpretations - to stop falling for errors like that,

Its truth is entirely interpretation dependent.

Thanks
Bill

#### PeterDonis

Mentor
in quantum physics there is an additional fundamental and irreducible component of randomness/probabilities in the underlying dynamics (God plays dice).
To amplify @bhobba's response a bit, this is only the case for "collapse" interpretations; it is not the case for the MWI and similar interpretations. So this statement is interpretation dependent.

#### meopemuk

To amplify @bhobba's response a bit, this is only the case for "collapse" interpretations; it is not the case for the MWI and similar interpretations. So this statement is interpretation dependent.
Isn't it true that in M(any)W(orlds)I(nterpretation) each measurement creates new Universes -- as many as there are possible measurement outcomes? But you -- the observer -- must jump into one of these Universes to get on with your life. And this jump is random. So, we are back to the fundamental irreducible randomness, this time with all the bells and whistles of multiple worlds.

As far as I can see, all QM interpretations have a random element in them. The crucial question: is this the true irreducible randomness (like in QM) or just the ignorance/laziness randomness (like in statistical mechanics)? In the former case, our interpretation hasn't added anything of value to the regular shut-up-and-calculate quantum mechanics. There is no experiment that can prove/disprove our interpretation. The latter case is more interesting, as it promises that one day we will learn how to handle these "hidden variables". Then we will be able to predict the exact timing sequence of clicks in the Geiger counter or the pattern of electron hits on the scintillating screen.

I choose the former answer, with the full understanding that this choice is based on belief, not on knowledge.

Eugene.

#### stevendaryl

Staff Emeritus
Bell doesn't take into account that a macroscopic measurement is actually done by recording field expectation values.
Well, that is certainly far from being an accepted resolution. I don't see how anything in his argument depends on that.

#### PeterDonis

Mentor
Isn't it true that in M(any)W(orlds)I(nterpretation) each measurement creates new Universes -- as many as there are possible measurement outcomes?
No. There is only one universe and one quantum state. But it contains subsystems that are entangled in a way that invites the ordinary language term "many worlds" because our ordinary language assumes that things are in ordinary classical states.

For example, if you watch a Stern-Gerlach experiment measuring the spin of an electron, your quantum state becomes entangled with the electron's so that, heuristically, in the universal wave function, there are two terms, one a product of "electron spin up" and "you observe electron spin up", and the other a product of "electron spin down" and "you observe electron spin down". Since our ordinary language concept of "you" assumes that you observed only one result, this kind of quantum state invites the ordinary language description that there are now two "copies" of you (and the electron).

And since stuff like this is happening all the time, everywhere in the universe, it invites the ordinary language description that there are multiple "universes". But there is still only one quantum state--one wave function--and as far as the math of QM is concerned, that is one universe, one "world", not many. Nothing gets "created" during a measurement, because everything is unitary, and unitary operations don't create or destroy anything.

#### meopemuk

No. There is only one universe and one quantum state.
But still, even within MWI, there should be a point where a choice must be made, which copy of myself -- the observer -- is the real one. Whether the electron went up or down in this particular instance? So, we are back to the random collapse. I am not sure what is collapsing in this case, but Nature makes a random choice between a number of possibilities. I call it a collapse.

So, all the elaborate mechanisms of MWI have bought us absolutely nothing. We are still staring at the fundamental irreducible randomness of Nature.

Eugene.

#### PeterDonis

Mentor
But still, even within MWI, there should be a point where a choice must be made, which copy of myself -- the observer -- is the real one
Nope. In the MWI, the wave function is real, and there is one wave function. There is no choice to be made.

Whether the electron went up or down in this particular instance?
It went in both directions. In the MWI, measurements do not have single results; they have all possible results.

all the elaborate mechanisms of MWI have bought us absolutely nothing. We are still staring at the fundamental irreducible randomness of Nature.
You are incorrect. The MWI is not easy to come to terms with, but what it says is perfectly straightforward, and it completely eliminates randomness. The question is whether it is true; we don't know since we have no way of testing it experimentally (since it makes the same predictions for the results of measurements as all other interpretations of QM--which it must since it uses the same math).

#### meopemuk

In the MWI, measurements do not have single results; they have all possible results.
But in reality measurements do have single results. Then how does MWI relates to reality?

Eugene.

#### PeterDonis

Mentor
in reality measurements do have single results.
Not if the MWI is true. If the MWI is true, all possible results happen, and each result is entangled with the appropriate state of measuring devices, observers, etc., so that, for example, all possible experiences you can have observing the different possible results of a measurement also happen. You are only aware of one result because your awareness depends on your brain state, and the different branches of the wave function have different states for your brain, just as they have different states for the measured system.

In other words, according to the MWI, we don't actually know that "in reality", measurements have single results. All we know is that we observe measurements to have single results. The MWI accounts for this the way I explained just above--by treating our observations, our experiences, as part of the universal wave function, so they get entangled, superposed, etc., just like everything else.

I understand that this is difficult to wrap your mind around. But any discussion of interpretations of QM has to take it into account.

#### meopemuk

In other words, according to the MWI, we don't actually know that "in reality", measurements have single results. All we know is that we observe measurements to have single results. The MWI accounts for this the way I explained just above--by treating our observations, our experiences, as part of the universal wave function, so they get entangled, superposed, etc., just like everything else.
Thank you for explaining this. If so, then the MWI is the weirdest kind of philosophy. I remember learning that there are two major schools of philosophy:

Materialism says that things happen in the real world, and our perceptions are just reflections of these objective events. I am cool with that.

Idealism says that the real world is just an illusion, and all we have are our perceptions. I can accept even that.

But now, there is the MWI, which says that even our perceptions are illusions, and there is nothing but the super-entangled MWI wave function. How weird is that!

Eugene.

#### PeterDonis

Mentor
there is the MWI, which says that even our perceptions are illusions
No, they're not illusions. When you perceive an electron coming out of the "spin up" side of a Stern-Gerlach device, that's because the branch of the electron's wave function that that branch of your brain is entangled with is coming out of the "spin up" side of the device. All of the entanglements match up just the way they should for the results you perceive to be correct.

there is nothing but the super-entangled MWI wave function
The MWI doesn't say there is "nothing but" the wave function. It just says that everything is "made of" the wave function, the same way classical atomic theory said everything was made of atoms. The MWI does not say that you and I don't exist. It just says that what we are actually referring to by the words "you" and "I" is not as simple as our naive intuitions tell us it is.

#### meopemuk

When you perceive an electron coming out of the "spin up" side of a Stern-Gerlach device, that's because the branch of the electron's wave function that that branch of your brain is entangled with is coming out of the "spin up" side of the device.
Sorry for being so slow. But I just don't get it.

I understand that there is a part of my brain's wave function entangled with the "spin up" electron. I can also accept that there is another piece/part/branch of my brain entangled with the "spin down" electron. But when I looked at the Stern-Gerlach device last time I can swear I saw only the "spin up". So, where did the other ("spin down") portion disappeared? In another Universe?

I don't care whether the "spin down" portion disappeared in reality, or only in my perception. For me it did disappear, because I didn't see it. I don't care if both up and down portions exist in the MWI wave function (maybe in different Universes). I would like to have a theory that describes for me what I see (or what I think I see) in my Universe. And I see that the up and down outcomes occur in some random pattern, if I keep repeating my experiment. But the MWI tries to convince me that both outcomes coexist. Then who is right, me -- the observer -- or the MWI?

Eugene.

#### PeterDonis

Mentor
when I looked at the Stern-Gerlach device last time I can swear I saw only the "spin up". So, where did the other ("spin down") portion disappeared? In another Universe?
The problem is that word "I". You are using it like it refers to the entire "piece" of the wave function that corresponds to your brain. But it doesn't. It only refers to the part of your brain's wave function that got entangled with the spin up part of the electron's wave function. There is another part of your brain's wave function that got entangled with the spin down part of the electron's wave function; and that part of your brain's wave function uses the word "I" to refer to itself, just as the part you are thinking of in the quote above, the part that got entangled with the spin up part of the electron's wave function, uses the word "I" to refer to itself. So the problem is that there is only one word, "I", but it's doing double duty. This is very confusing, of course, but it's what we get for trying to use ordinary language to describe something that ordinary language has no proper terminology to describe.

I would like to have a theory that describes for me what I see (or what I think I see) in my Universe.
The MWI does do that; it tells "you" that "you" will observe whatever is consistent with the states of the observed object that "your" brain gets entangled with. But the referent of the word "you" has to be clearly understood. See above.

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